There were no reports of any injuries in the incident and AirAsia X did not respond immediately to a request for comment.
AirAsia said in a statement on its official Twitter account the flight was diverted "after experiencing a suspected bird strike to its starboard engine shortly after takeoff".
"Two bird remains were found on the runway," it said.
Passengers said the plane began shaking shortly after take-off.
"The plane started shuddering then there were a couple of loud bangs and a lot of light," Tim Joga told the Sydney Morning Herald newspaper. Another passenger told the paper she saw flames coming from the right engine.
The plane was forced to land 100 km (60 miles) away at Brisbane, the Queensland capital, just 11.30 p.m. local time (1430 GMT), a spokesman for Australia's Civil Aviation Safety Authority (CASA) said.
The CASA spokesman said AirAsia's engineers were expected to confirm the cause of the problem later on Tuesday.
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